A278996 Numbers of the form (3h+1)*3^(2k)-1 or (3h+2)*3^(2k+1)-1 for h,k in N.

0, 3, 5, 6, 8, 9, 12, 14, 15, 18, 21, 23, 24, 27, 30, 32, 33, 35, 36, 39, 41, 42, 45, 48, 50, 51, 53, 54, 57, 59, 60, 62, 63, 66, 68, 69, 72, 75, 77, 78, 80, 81, 84, 86, 87, 89, 90, 93, 95, 96, 99, 102, 104, 105, 108, 111, 113, 114, 116, 117, 120, 122, 123, 126, 129, 131

Offset: 1

Author

N. J. A. Sloane, Dec 07 2016

Keywords

• nonn

Comments

n is in the sequence if and only if either n == 0, 3, 5, or 6 (mod 9) or n == 8 (mod 9) and (n-8)/9 is in the sequence. - Robert Israel, Dec 15 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Hao Fu, G.-N. Han, Computer assisted proof for Apwenian sequences related to Hankel determinants, arXiv preprint arXiv:1601.04370 [math.NT], 2016. See sequence "J" in Section 2.1.

Crossrefs

Complement of A278997.

Programs

Maple

filter:= proc(n) local m;
  m:= padic:-ordp(n+1,3);
  (n+1)/3^m mod 3 = 1 + (m mod 2)
end proc:
select(filter, [$0..100]); # Robert Israel, Dec 15 2016

Mathematica

isok[n_]:=Module[{ord=IntegerExponent[n+1,3]},Mod[(n+1)/3^ord,3]==Mod[ord,2]+1];Select[Range[0,131],isok](* Ray Chandler, Dec 17 2016 *)

Extensions

More terms from Robert Israel, Dec 15 2016